They are also applying for declarations that there have been violations of article four of the European Convention on Human Rights, which prohibits forced labour and slavery.

The DWP says the schemes - the Community Action Programme and Work Academy Scheme - are not slave labour but play an important part in giving jobseekers the skills and experience they need to find work.

"It is entirely reasonable to ask jobseekers to take real steps towards finding work if they are claiming benefits," the DWP said in a statement.

A judge at London's High Court was told by Ms Reilly's QC that the geology graduate's stint at the Poundland near her home in Kings Heath, Birmingham, involved her carrying out "unpaid menial work".

This consisted of very basic tasks such as sweeping and shelf-stacking "without training, supervision or remuneration".

She had signed up to a Work Academy Scheme open day unaware that it would require her to work for free at Poundland last November.

Nathalie Lieven QC submitted to Mr Justice Foskett: "Such work did not contribute to (Ms Reilly's) search for work to any extent."

The graduate had only participated because she was told the training was mandatory and she risked losing her jobseeker's allowance or having it reduced if she did not attend.

Ms Lieven said Ms Reilly graduated from Birmingham University in 2010 and first claimed jobseeker's allowance in August that year soon after graduation.

She hoped to work in museums and was now undertaking voluntary work at a local museum.

No-one had questioned her level of effort in seeking employment and she had been happy to look for paid work in the retail sector.

Ms Reilly had been told the programme involved not only training but a job interview at the end of the training period, but there was no interview.

The second challenge before the court involves Jamieson Wilson, a 40-year-old unemployed HGV driver from the Midlands who has been claiming benefits since 2008.

Ms Lieven said Mr Wilson was told last November he would be required to undertake 30 hours' unpaid work a week for up to six months cleaning furniture, and further periods of required work could follow.

Ms Lieven said Mr Wilson had recently been subjected to sanctions after refusing to take part in the scheme and now apparently faced the loss of jobseeker's allowance for six months.